1. Mathematical and Boolean basics and circuits

• induction, recursion, and recurrences
• graph terminology and properties: directed acyclic
• basis, addition, carry-look-ahead, multiplication, MUX

- Basic mathematical data types and operations

• boolean, non-negative integer, integer, character
• representation in digital computer
• algorithmic primitives

- Combining mathematical data types

• tuple, finite sequence, un/directed labeled graph
• representation in digital computer

- Computational problems and algorithmic solutions

• polynomial multiplication, matrix multiplication
• asymptotic growth, recurrences and their solutions

- Searching and Sorting

• linear search, binary search, bubble sort, bucket s * Unordered List Itemort
• specification and analysis of the above algorithms
• mergesort, quicksort, linear-time median
• lower bound for comparison-based sorting

- Linked Data Structures

• lists: singly/doubly-linked; search/traverse, insert/delete
• queue=FiFo, stack=LiFo
• binary trees: terminology, BFS/DFS/search, insert/delete/balance

- Basic Graph Problems and Algorithms

• Un-/directed graph terminology and properties
• Shortest unweighted path: BFS
• single source shortest weighted path: Dijkstra

- Abstract Data Types and their implementations

• stack, queue, priority queue, dynamic array, …